Pith Number

pith:YZDA372M

pith:2025:YZDA372M6HR3B2LE2QV2JCOSWB

not attested not anchored not stored refs pending

Ultracategories as colax algebras for a pseudo-monad on CAT

Ali Hamad

arxiv:2502.20597 v3 · 2025-02-27 · math.CT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YZDA372M6HR3B2LE2QV2JCOSWB}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Cited by

1 paper in Pith

Extending conceptual completeness via virtual ultracategories

Receipt and verification

First computed	2026-07-05T11:58:25.493532Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c6460dff4cf1e3b0e964d42ba489d2b0445fb99bf68f0c38c9b914c07b900561

Aliases

arxiv: 2502.20597 · arxiv_version: 2502.20597v3 · doi: 10.48550/arxiv.2502.20597 · pith_short_12: YZDA372M6HR3 · pith_short_16: YZDA372M6HR3B2LE · pith_short_8: YZDA372M

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/YZDA372M6HR3B2LE2QV2JCOSWB \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: c6460dff4cf1e3b0e964d42ba489d2b0445fb99bf68f0c38c9b914c07b900561

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19e31f0e98ee4224ea57a084159b13b3c5114060a9eef2d528391d7d459178c8",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2025-02-27T23:55:14Z",
    "title_canon_sha256": "5108468c1c4552aeba2a5e254739898b6c03e7e2fc3158feb4820a9fad66a0b0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2502.20597",
    "kind": "arxiv",
    "version": 3
  }
}